Topological Quantum Field Theory Seminar   RSS

26/05/2014, 15:30 — 16:30 — Room P3.10, Mathematics Building
, Thammasat University, Bangkok, Thailand

Higher Categories of Operator Algebras

A satisfactory marriage between “higher” categories and operator algebras has never been achieved: although (monoidal) C*-categories have been systematically used since the development of the theory of superselection sectors, higher category theory has more recently evolved along lines closer to classical higher homotopy.

We present axioms for strict involutive \(n\)-categories (a vertical categorification of dagger categories) and a definition for strict higher C*-categories and Fell bundles (possibly equipped with involutions of arbitrary depth), that were developed in collaboration with Roberto Conti, Wicharn Lewkeeratiyutkul and Noppakhun Suthichitranont.

In order to treat some very natural classes of examples arising from the study of hypermatrices and hyper-C*-algebras, that would be otherwise excluded by the standard Eckmann-Hilton argument, we suggest a non-commutative version of exchange law and we also explore alternatives to the usual globular and cubical settings.

Possible applications of these non-commutative higher C*-categories are envisaged in the algebraic formulation of Rovelli's relational quantum theory, in the study of morphisms in Connes' non-commutative geometry, and in our proposed “modular” approach to quantum gravity (arXiv: 1007.4094).

Note: unusual time/day and room

To join the session on Zoom a password is required. If you are not already on the mailing list, please subscribe the announcements to receive password info and updates.

Current organizers: José MourãoRoger Picken, Marko Stošić


FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.